1. Field of the Invention
This invention relates to a voltage stability discrimination system for a power system for use in calculating a pair of multiple load flow solutions which are closely located each other concerning the voltage stability discrimination for the power system.
2. Description of the Prior Art
As recent power systems have become large and complicated, it is sometimes found that a limitation on the system's stability may be determined by a voltage stability as well as a dynamic stability of power generators. FIG. 1 is a load-voltage curve (hereinafter called a P-V curve), wherein if the power system has characteristics as shown by a curve A and the load is set at P.sub.1, the two load flow solutions become A.sub.1 and A.sub.2. The fact that A.sub.1 and A.sub.2 are adjacent to each other as shown in this diagram means that the Power P.sub.A is the stability limit and beyond this Point voltage collapse may occur. In turn, in the curve B, the two load flow solutions are B.sub.1 and B.sub.2. (The solution B.sub.2 is not present in a certain case.) Since the solutions B.sub.1 and B.sub.2 are located apart as compared with those shown in the curve A, they are far from representing a stability limit in transmitting power P.sub.B where the voltage collapse starts to occur and they have a voltage stability. In view of this fact, although the voltage stability has a close relation with a pair of multiple load flow solutions and some researchers have investigated for a method of resolving multiple solutions so as to get some effects, it is desired to make a robust and fast calculating method for finding a multiple load flow solution (a lower solution) which locates nearby a normal operating voltage solution (a higher solution) because such a solution may have a bad influence on the voltage stability.
In view of the foregoing, applicants will describe a method of finding a pair of load flow solutions in the prior art voltage stability discrimination system for the power system indicated in "A method for Finding Multiple Load-Flow Solutions for General Power Systems" by Tamura, Iba and Iwamoto, IEEE paper No. A80 043-0 presented at the IEEE PES Winter Meeting, New York, N.Y., February 3-8, 1980.
A current basic equation of a P-th bus line in n-th bus line system can be expressed as follows by applying rectangular coordinates. ##EQU1## EQU .vertline.V.sub.p .vertline..sup.2 =e.sub.p.sup.2 +f.sub.p.sup.2( 3)
where, ##EQU2##
Then, the first and second equations are rewritten to the following equations (4) and (5): EQU P.sub.p =G.sub.pp (e.sub.p.sup.2 +f.sub.p.sup.2)+A.sub.pcp +B.sub.pfp( 4) EQU Q.sub.p =B.sub.pp (e.sub.p.sup.2 +f.sub.p.sup.2)-B.sub.pep +A.sub.pfp( 5)
provided that ##EQU3##
Further, the values of A.sub.p and B.sub.p are assumed to be fixed and they are rewritten into a standard form of a circle as follows: ##EQU4## and then solutions of the above-mentioned simultaneous equations (6) and (7) are obtained In the prior art system, such local information above has been applied and a plurality of initial values for the multiple load flow solution calculation means have been prepared. Multiple load flow solutions have then been determined under several repetitions of calculation.
A voltage collapse suddenly occurs even if a severe contingency does not occur, and once the voltage collapse starts to continue, the conventional voltage controlling procedure may be not just scarcely effective, but rather it shows an inverse effect Due to this fact, it was necessary to get a fast and accurate calculation of a pair of multiple load flow solutions, a discrimination of a voltage stability, and fast control actions to generators, load shedding and lock of automatic adjustment control of transformers. However, the calculation of multiple load flow solutions in the voltage stability discrimination system in the prior art power system had to generate several initial values and repeat the conventional load flow calculation under a trial and error basis In general, there was a problem that the previous method required a lot of computing time to find multiple load flow solutions.